Flying and facing

[Celebrim]

Suppose a gargantuan dragon (a clumsy flier) is airborn in a fight with a group of PC's, and has just moved in a straight line from a position 140' north of the PC's and 50' above the ground to a position 60' south of the PC's and 40' above the ground - straffing the PC's with its breath weapon in a Fly By attack along the way. A PC with the capacity of flight and sufficient movement decides to charge the dragon and finish its move in the square nearest the PC's starting position but adjacent to the dragon.

Supposing that the dragon's tail has been loped off by the parties sword of sharpness, does the dragon threaten the squares in the direction that the PC is in, and therefore is eligible to make an AoO? Why or why not?

After the PC charges, can the dragon make a claw attack on the PC without changing direction? Suppose the Dragon has the Hover feat, does this change your answer? Why or why not?

 

[Infiniti2000]

A PC with the capacity of flight and sufficient movement decides to charge the dragon and finish its move in the square nearest the PC's starting position but adjacent to the dragon.

I don't think the PC can charge the dragon in such a way unless the PC has perfect manueverability. He can only move half speed, that's for sure, and I think that negates the possibility of a charge (he's essentially hindered). This is arguable, though.

Supposing that the dragon's tail has been loped off by the parties sword of sharpness, does the dragon threaten the squares in the direction that the PC is in, and therefore is eligible to make an AoO? Why or why not?

The dragon still threatens all squares around him. His movement is limited in terms of direction, but nothing in the rules suggests he can't attack creatures around him.

After the PC charges, can the dragon make a claw attack on the PC without changing direction? Suppose the Dragon has the Hover feat, does this change your answer? Why or why not?

Yes, but without hover, the dragon would then need to move half his speed (and thus provoke an AoO). With hover, he could just stay there and full attack. In actuality, even without hover, the dragon could full attack, but then he would fall to the ground (perhaps a worthwhile tactic if he had a ring of featherfalling, or just the spell).